Author

# Balth. van der Pol

Bio: Balth. van der Pol is an academic researcher from Philips. The author has contributed to research in topics: Amplitude & Point source. The author has an hindex of 13, co-authored 21 publications receiving 1141 citations.

##### Papers

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Philips

^{1}TL;DR: In this article, forced oscillations in a circuit with non-linear resistance were studied. But the authors focused on the reception with reactive triodes. And they did not consider the effects of the reactive triode on the circuit.

Abstract: (1927). VII. Forced oscillations in a circuit with non-linear resistance. (Reception with reactive triode) The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 3, No. 13, pp. 65-80.

516 citations

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Philips

^{1}01 May 1946-Journal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering

145 citations

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Philips

^{1}TL;DR: In this article, it was shown that the field in the first medium, apart from the direct radiation from the point source, can be described as due to secondary waves originating in the integration space mentioned, the amplitude of these secondary waves being determined by the amplitude amplitude of a primary wave which can be considered to spread from the geometrical image of a point source with a propagation constant and absorption belonging to the second medium.

Abstract: The investigation starts from the rather complicated integral expressions given by Sommerfeld, Weyl and Bateman for the Hertzian functions (1) and (2) for the field at B(zb, ϱ0, o) in the first medium, due to an electric or magnetic dipole placed also in the first medium at A(za, o, o) above an infinitely extending but finitely conducting mirror (or earth) (second medium). Instead of obtaining approximations for these expressions or developing them in series, (as has been done by several investigators) which still lead to very complicated mathematical expressions without much physical transparency, the writer obtains a solution without any approximations whatsoever in the form of a space integral (15) and (17) having exactly the same form for the magnetic and electric case. The integration extends over the part of space occupied by the second medium below the geometrical image. It is shown that the field in the first medium, apart from the direct radiation from the point source, can be described as due to secondary waves originating in the integration space mentioned, the amplitude of these secondary waves being determined by the amplitude of a primary wave which can be considered to spread from the geometrical image of the point source with a propagation constant and absorption belonging to the second medium. The higher the conductivity of this second medium, the more the primary wave is therefore concentrated near the image of the point source until, for infinite conductivity, it is wholly concentrated at the image itself. Thus a mathematical approximation given by Sommerfeld and Weyl is extended and it is given a physical basis. From the theory developed a certain analogy between 1°. a perfectly smooth but finitely conducting mirror and 2°. an infinitely conducting but not perfectly smooth mirror is difficult to be denied.

136 citations

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Philips

^{1}TL;DR: In this article, the diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to badiotelegraphy and the theory of the rainbow, is discussed.

Abstract: (1937). XIII. The diffraction of electromagnetic waves from an electrical point source round a finitely conducting sphere, with applications to badiotelegraphy and the theory of the rainbow.— Part I. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 24, No. 159, pp. 141-176.

74 citations

##### Cited by

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Hunter College

^{1}TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.

Abstract: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >

3,568 citations

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TL;DR: The connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis are described.

Abstract: [1] The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.

2,116 citations

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01 Apr 1992TL;DR: The concept of instantaneous frequency (IF), its definitions, and the correspondence between the various mathematical models formulated for representation of IF are discussed in this paper, and the extent to which the IF corresponds to the intuitive expectation of reality is also considered.

Abstract: The concept of instantaneous frequency (IF), its definitions, and the correspondence between the various mathematical models formulated for representation of IF are discussed. The extent to which the IF corresponds to the intuitive expectation of reality is also considered. A historical review of the successive attempts to define the IF is presented. The relationships between the IF and the group-delay, analytic signal, and bandwidth-time (BT) product are explored, as well as the relationship with time-frequency distributions. The notions of monocomponent and multicomponent signals and instantaneous bandwidth are discussed. It is shown that these notions are well described in the context of the theory presented. >

1,952 citations

01 Jan 1992

TL;DR: In this paper, the concept of instantaneous frequency (IF) is extended to discrete-time signals, and the specific problem of estimating the IF of frequency-modulated (FM) discrete time signals embedded in Gaussian noise is explored.

Abstract: For pt.I see ibid., vol.80, no.4, p.520-38 (1992). The concept of instantaneous frequency (IF) is extended to discrete-time signals. The specific problem explored is that of estimating the IF of frequency-modulated (FM) discrete-time signals embedded in Gaussian noise. Well-established methods for estimating the IF include differentiation of the phase and smoothing thereof, adaptive frequency estimation techniques such as the phase locked loop (PLL), and extraction of the peak from time-varying spectral representations. More recently, methods based on a modeling of the signal phase as a polynomial have been introduced. These methods are reviewed, and their performance compared on both simulated and real data. Guidelines are given as to which estimation method should be used for a given signal class and signal-to-noise ratio (SNR). >

1,260 citations

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01 Jun 1990TL;DR: In this paper, a more general averaging procedure that encompasses state-space averaging and that is potentially applicable to a much broader class of circuits and systems is presented, including resonant type converters.

Abstract: A more general averaging procedure that encompasses state-space averaging and that is potentially applicable to a much broader class of circuits and systems is presented. Examples of its application in resonant and PWM power convertors are presented. The technique is shown to be effective on a number of examples. including resonant type converters. The approach offers refinements to the theory of state-space averaging, permitting a framework for analysis and design when small ripple conditions do not hold. The method may find applications in simulation and design since it is considerably easier to simulate an averaged model than a switched model. >

1,144 citations